The flight of a golf ball is determined by many factors. The majority of the properties that determine flight are outside of the control of the golfer. While a golfer can control the speed, the launch angle, and the spin rate of a golf ball by hitting the ball with a particular club, the final resting point of the ball depends upon golf ball construction and materials, as well as environmental conditions, e.g., terrain and weather. Since flight distance and consistency are critical factor in reducing golf scores, manufacturers continually strive to make even the slightest incremental improvements in golf ball flight consistency and flight distance, e.g., one or more yards, through various aerodynamic properties and golf ball constructions. For example, golf balls were originally made with smooth outer surfaces. However, in the late nineteenth century, players observed that, as golf balls became scuffed or marred from play, the balls achieved more distance. As such, players then began to roughen the surface of new golf balls with a hammer to increase flight distance.
Manufacturers soon caught on and began molding non-smooth outer surfaces on golf balls. By the mid 1900's, almost every golf ball being made had 336 dimples arranged in an octahedral pattern. Generally, these balls had about 60 percent of their outer surface covered by dimples. Over time, improvements in ball performance were developed by utilizing different dimple patterns. In 1983, for instance, Titleist introduced the TITLEIST 384, which had 384 dimples that were arranged in an icosahedral pattern resulting in about 76 percent coverage of the ball surface. The dimpled golf balls used today travel nearly two times farther than a similar ball without dimples.
These improvements have come at great cost to manufacturers. In fact, historically manufacturers improved flight performance via iterative testing, where golf balls with numerous dimple patterns and dimple profiles are produced and tested using mechanical golfers. Flight performance is characterized in these tests by measuring the landing position of the various ball designs. For example, to determine if a particular ball design has desirable flight characteristics for a broad range of players, i.e., high and low swing speed players, manufacturers perform the mechanical golfer test with different ball launch conditions, which involves immense time and financial commitments. Furthermore, it is difficult to identify incremental performance improvements using these methods due to the statistical noise generated by environmental conditions, which necessitates large sample sizes for sufficient confidence intervals.
Another more precise method of determining specific dimple arrangements and dimple shapes, that result in an aerodynamic advantage, involves the direct measurement of aerodynamic characteristics as opposed to ball landing positions. These aerodynamic characteristics define the forces acting upon the golf ball throughout flight.
Aerodynamic forces acting on a golf ball are typically resolved into orthogonal components of lift (FL) and drag (FD). FIG. 1 shows the various forces acting on a golf ball in flight. Lift is defined as the aerodynamic force component acting perpendicular to the flight path. It results from a difference in pressure that is created by a distortion in the air flow that results from the back spin of the ball. A boundary layer forms at the stagnation point of the ball, B, then grows and separates at points S1 and S2, as shown in FIG. 2. Due to the ball backspin, the top of the ball moves in the direction of the airflow, which retards the separation of the boundary layer. In contrast, the bottom of the ball moves against the direction of airflow, thus advancing the separation of the boundary layer at the bottom of the ball. Therefore, the position of separation of the boundary layer at the top of the ball, S1, is further back than the position of separation of the boundary layer at the bottom of the ball, S2. This asymmetrical separation creates an arch in the flow pattern, requiring the air over the top of the ball to move faster and, thus, have lower pressure than the air underneath the ball.
Drag is defined as the aerodynamic force component acting parallel to the ball flight direction. As the ball travels through the air, the air surrounding the ball has different velocities and, accordingly, different pressures. The air exerts maximum pressure at the stagnation point, B, on the front of the ball, as shown in FIG. 2. The air then flows over the sides of the ball and has increased velocity and reduced pressure. The air separates from the surface of the ball at points S1 and S2, leaving a large turbulent flow area with low pressure, i.e., the wake. The difference between the high pressure in front of the ball and the low pressure behind the ball reduces the ball speed and acts as the primary source of drag for a golf ball.
The dimples on a golf ball are important in reducing drag and increasing lift. For example, the dimples on a golf ball create a turbulent boundary layer around the ball, i.e., the air in a thin layer adjacent to the ball flows in a turbulent manner. The turbulence energizes the boundary layer and helps it stay attached further around the ball to reduce the area of the wake. This greatly increases the pressure behind the ball and substantially reduces the drag.
Based on the role that dimples play in reducing drag on a golf ball, golf ball manufacturers continually seek dimple patterns that increase the distance traveled by a golf ball. A high degree of dimple coverage is beneficial to flight distance, but only if the dimples are of a reasonable size. Dimple coverage gained by filling spaces with tiny dimples is not very effective, since tiny dimples are not good turbulence generators.
In addition to researching dimple pattern and size, golf ball manufacturers also study the effect of dimple shape, volume, and cross-section on overall flight performance of the ball. One example is U.S. Pat. No. 5,735,757, which discusses making dimples using two different spherical radii with an “inflection point” where the two curves meet. In most cases, however, the cross-sectional profiles of dimples in prior art golf balls are spherical, parabolic, elliptical, semi-spherical curves, saucer-shaped, a sine curve, a truncated cone, or a flattened trapezoid. One disadvantage of these shapes is that they can sharply intrude into the surface of the ball, which may cause the drag to become excessive. As a result, the ball may not make best use of momentum initially imparted thereto, resulting in an insufficient carry of the ball.
Further, the most commonly used spherical profile is essentially a function of two parameters: diameter and depth (chordal or surface). While edge angle, which is a measure of the steepness of the dimple wall where it abuts the ball surface, is often discussed when describing these types of profiles, edge angle generally cannot be varied independently of depth unless dual radius profiles are employed. The cross sections of dual radius dimple profiles are generally defined by two circular arcs: the first arc defines the outer part of the dimple and the second arc defines the central part of the profile. The radii are typically larger in the center, which produces a saucer shaped dimple where the steepness of the walls (and, thus, the edge angle) may be varied independently of the dimple depth and diameter. While effective, this profile is described by a number of equations that at least require first order continuity for tangency between the arcs, as well as varying dimple diameter and depth values to achieve the desired dimple shape.
In addition to the profiles discussed above, dimple patterns have been employed in an effort to control and/or adjust the aerodynamic forces acting on a golf ball. For example, U.S. Pat. Nos. 6,213,898 and 6,290,615 disclose golf ball dimple patterns that reduce high-speed drag and increase low speed lift. It has now been discovered, however, contrary to the disclosures of these patents, that reduced high-speed drag and increased low speed lift does not necessarily result in improved flight performance. For example, excessive high-speed lift or excessive low-speed drag may result in undesirable flight performance characteristics. The prior art is silent, however, as to aerodynamic features that influence other aspects of golf ball flight, such as flight consistency, as well as enhanced aerodynamic coefficients for balls of varying size and weight.
Thus, there remains a need to optimize the aerodynamics of a golf ball to improve flight distance and consistency. Further, there is a need to develop dimple arrangements and profiles that result in longer distance and more consistent flights regardless of the swing-speed of a player, the orientation of the ball when impacted, or the physical properties of the ball being played. The use of catenary dimple profiles is considered one way to achieve these objectives.